In Problems 51-56, solve for x.

Name: Problem 53, Chapter 8: College Algebra
Uploaded: 2021-08-30T17:47:06-08:00
Duration: 3 min 24 s
Channel: Taimoor Shabbir
Description: In Problems 51-56, solve for x. | x 1 1 4 3 2 -1 2 5 |=2

step 1 in this problem we have to solve this 3 by 3 determinant and find the value of x so we will use

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Key Concepts

Determinant of a Matrix

The determinant is a scalar value that is computed from a square matrix and encapsulates important properties about the matrix such as invertibility and volume scaling in linear transformations. In the context of solving equations, a nonzero determinant indicates an invertible matrix, and setting the determinant equal to a specific value can lead to an equation to solve for unknown parameters in the matrix.

Computing a 3x3 Determinant

For a 3x3 matrix, the determinant can be calculated using methods such as cofactor expansion or by applying the rule of Sarrus. In this method, the determinant is expressed in terms of the elements of the matrix, and expanding along a row or column breaks the determinant down into 2x2 sub-determinants.

Solving Equations Involving Determinants

When a determinant expression involving a variable is set equal to a constant, it leads to an algebraic equation in that variable. Solving such equations involves expanding the determinant to obtain an equation, simplifying it, and then solving for the unknown variable, which is a common application in linear algebra.

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